三维椭圆型方程S-COR算法的收敛性估计

给出求解三维椭圆方程的一个异步算法（S－COR算法）的收敛性分析。在很弱的条件下，证明了算法的收敛性，并得到了一个收敛速度估计：如果对某一迭代中间过程，在该过程中每个子问题都至少被求解一次，则经过该迭代过程后误差以某一固定常数衰减，并且显式给出该常数与有限元网格直径和处理机台数的关系。

Convergence Estimates to the S-COR Algorithm for Solving Three Dimensional Elliptic Equations

This paper gave the convergence analysis to an asynchronous algorithm (S COR algorithm) for solving three dimensional elliptic equations. Under the very weak conditions, the algorithm was proved to be convergent. Moreover, the convergence rate estimate was also obtained, that is, for any iteration period with the property that each sub problem is solved at least one time during the period, the error will decrease with a fixed constant after this iteration period. The explicit relation of the fixed constant to the diameters of the finite elements and the number of processors was also provided.